Let D be an integral domain with quotient field K. In [1], the authors called D a finitely valuative domain if, for each $0{ eq}u{in}K$, there is a saturated chain of rings $D=D_0{varsubsetneq}D_1{varsubsetneq}{cdots}{subseteq}$ $D_n=D[x]$, where x = u or $u^{-1}$. They then studied some properties of finitely valuative domains. For example, they showed that the integral closure of a finitely valuative domain is a Pr$ddot{u}$fer domain. In this paper, we introduce the notion of finitely t-valuative domains, which is the t-operation analog of finitely valuative domains, and we then generalize some properties of finitely valuative domains.